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Chapter 6: Problem 2

Solve each proportion for \(x\) a. \(\frac{2}{9}=\frac{x}{108}\) b. \(\frac{8}{7}=\frac{120}{x}\) c. \(\frac{x}{20}=\frac{70}{100}\)

Short Answer

Expert verified
a. \(\frac{2}{9}=\frac{x}{108}\) b. \(\frac{8}{7}=\frac{120}{x}\) c. \(\frac{x}{20}=\frac{70}{100}\) Answer: The values of \(x\) are: a. \(x = 24\) b. \(x = 105\) c. \(x = 14\)

Step by step solution

01

a. Solving the proportion \(\frac{2}{9}=\frac{x}{108}\)

Step 1: Cross-multiply In this step, we will cross-multiply the proportions. \((2)(108) = (9)(x)\) Step 2: Simplify the equation After cross-multiplying, we have: \(216 = 9x\) Step 3: Solve for \(x\) Divide both sides of the equation by 9: \(x = \frac{216}{9}\) Step 4: Simplify further \(x = 24\)
02

b. Solving the proportion \(\frac{8}{7}=\frac{120}{x}\)

Step 1: Cross-multiply In this step, we will cross-multiply the proportions. \((8)(x) = (7)(120)\) Step 2: Simplify the equation After cross-multiplying, we have: \(8x = 840\) Step 3: Solve for \(x\) Divide both sides of the equation by 8: \(x = \frac{840}{8}\) Step 4: Simplify further \(x = 105\)
03

c. Solving the proportion \(\frac{x}{20}=\frac{70}{100}\)

Step 1: Cross-multiply In this step, we will cross-multiply the proportions. \((x)(100) = (20)(70)\) Step 2: Simplify the equation After cross-multiplying, we have: \(100x = 1400\) Step 3: Solve for \(x\) Divide both sides of the equation by 100: \(x = \frac{1400}{100}\) Step 4: Simplify further \(x=14\) So, the solutions are \(x = 24\) for a, \(x = 105\) for b, and \(x = 14\) for c.

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Most popular questions from this chapter

The admissions office in a local college has organized data in the following table listing the number of men and women who are currently enrolled. Admissions will use the data to help recruit students for the next academic year. Note that a student is matriculated if he or she is enrolled in a program that leads to a college degree. $$\begin{array}{|c|c|c|} \hline {} & \text { FULL-TIME } & \text { PART-TIME } & \text { PART-TIME } \\\ {} & \text { MATRICULATED } & \text { MATRICULATED } & \text { NONMATRICULATED} \\\ {} & \text { STUDENTS } & \text { STUDENTS } & \text { STUDENTS } \\\ {} & ( \geq 12 \text { Credits) } & ( < 12 \text { Credits) } & ( < 12 \text { Credits) } \\\\\hline \text { Men } & 214 & 174 & 65 \\\ \hline \text { Women } & 262 & 87 & 29 \\\ \hline \end{array}$$ a. How many men attend the college? b. What percent of the men are full-time students? c. How many women attend the college? d. What percent of the women are full-time students? e. Write the ratio of men to women verbally and as a fraction. f. How many students are enrolled full-time? g. How many students are enrolled part-time? h. Write the ratio of part-time students to full-time students verbally and as a fraction. i. What percent of the full-time students are women? j. What percent of the part-time students are women? k. How many students are nonmatriculated? l. Write the ratio of nonmatriculated men to matriculated men verbally and as a fraction. m. What percent of the student body is nonmatriculated?
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